The 17-year-old goalkeeper, an England youth international, has impressed for the Magpies development squad in recent years, but the club have yet to offer him professional terms.
His scholarship deal expires at the end of the season, and the club have offered him a third-year scholarship deal, rather than professional terms.
As this could allow him to leave this summer for a tiny compensation fee, a number of Premier League sides who are interested in the keeper are ready to move for him.
Woolston, who started his career with Sunderland, joined Newcastle in 2013, and has made a name for himself in the following years.
He has been capped 14 times for England’s Under-17s, making his debut for the Under-18 side this season.
There are no clubs referenced in the report as looking to sign Woolston, but clearly many scouts have been impressed by the player who kept a clean sheet for the Magpies’ Under-21 side against Manchester United on his debut - aged just 15.
The Tyneside outfit do not feel as if the keeper is ready to earn a professional contract, and this could cause them to lose the stopper this summer.